Abstract
The stochastic‐deterministic approach to modeling of the Saffman–Taylor hydrodynamic instability in filtration of mixing fluids in a porous medium is considered. The numerical model is used to study the dynamics of development of the instability in displacement of a more viscous fluid by a less viscous one in uniformly and nonuniformly permeable media. Results of the modeling are compared to experimental data.
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REFERENCES
S. Hill, Chem. Eng. Sci., 1, No. 2, 247–253 (1952).
P. G. Saffman and G. Y. Taylor, Proc. Roy. Soc. (London), Ser. A, 245, No. 1242, 312–329 (1958).
R. L. Slobod and R. A. Thomas, Soc. Petrol. Eng. J., 3, 9–13 (1963).
B. Habermann, Trans. AIME, 219, 264–272 (1960).
R. L. Chouke, P. Van Meurs, and C. Van der Poel, Trans. AIME, 216, 188–194 (1959).
K. S. Sorbie, H. R. Zhang, and N. B. Tsibuklis, Chem. Eng. Sci., 50, No. 4, 601–616 (1995).
H. R. Zhang, K. S. Sorbie, and N. B. Tsibuklis, Chem. Eng. Sci., 52, No. 1, 37–54 (1997).
C. T. Tan and M. Zeybek, Phys. Fluids, 29, No. 11, 3549–3556 (1986).
Y. C. Yortsos and G. M. Homsy, Phys. Fluids, 31, No. 12, 3511–3518 (1988).
E. J. Koval, Soc. Petrol. Eng. J., 3, 145–154 (1963).
A. S. Odeh and M. F. Cohen, Energy Sources, 11, 9–17 (1989).
C. T. Tan and G. M. Homsy, Phys. Fluids, 31, No. 6, 1330–1338 (1988).
W. B. Zimmerman and G. M. Homsy, Phys. Fluids A, 4, No. 9, 1901–1914 (1992).
L. Paterson, Phys. Rev. Lett., 52, No. 18, 1621–1624 (1984).
H. Siddiqui and M. Sahimi, Chem. Eng. Sci., 45, No. 1, 163–182 (1990).
A. J. DeGregoria, Phys. Fluids, 28, No. 11, 2933–2935 (1985).
J. D. Sherwood and J. Nittmann, J. Physique, 47, 15–22 (1986).
M. D. Noskov and A. V. Rylin, Inzh.-Fiz. Zh., 73, No. 2, 267–273 (2000).
M. J. King and H. Scher, Phys. Rev. A, 41, No. 2, 874–883 (1990).
M. D. Noskov and A. D. Istomin, Mat. Modelir., 11, No. 10, 77–85 (1999).
G. I. Barenblatt and Yu. P. Zheltov, Dokl. Akad. Nauk SSSR, 132, No. 3, 545–548 (1960).
L. Lukner and V. M. Shestakov, Modeling of the Migration of Underground Water [in Russian], Moscow (1986).
S. K. Godunov and V. S. Ryaben'kii, Difference Schemes [in Russian], Moscow (1977).
A. A. Samarskii, Introduction to the Theory of Difference Schemes [in Russian], Moscow (1971).
K. J. Maloy, J. Feder, F. Boger, and T. Jossang, Phys. Rev. Lett., 61, No. 26, 2925–2928 (1988). 358
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Noskov, M.D., Istomin, A.D. & Kesler, A.G. Stochastic‐Deterministic Modeling of the Development of Hydrodynamic Instability in Filtration of Mixing Fluids. Journal of Engineering Physics and Thermophysics 75, 352–358 (2002). https://doi.org/10.1023/A:1015685420386
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DOI: https://doi.org/10.1023/A:1015685420386